8th Grade Slopes & Linear Equations Practice: Questions, Answers and Tips

Looking for 8th grade slopes & linear equations practice? Below are worked examples, the mistakes students make most, and practice questions with an answer key.

Every example below comes from BAMS Academy's Slopes & Linear Equations practice, the same questions students answer on the site.

Slopes & Linear Equations in 8th grade, skill by skill

Slope from points and graphs, slope-intercept and standard form, intercepts, writing equations, and parallel and perpendicular lines. BAMS Academy breaks the unit into the skills below (part of all 8th grade math topics). Each comes with one of its practice questions.

Standard form, slope-intercept form and intercepts

Which equation is 2x + 2y = −18 written in slope-intercept form? (Choices: y = −2x − 18; y = x − 9; y = −x + 9; y = −x − 9.)

Answer: y = −x − 9. Move the x-term: 2y = −2x − 18. Divide every term by 2: y = −x − 9.

Parallel and perpendicular lines

Which equation is a line parallel to the line shown in the graph? (Choices: y = x + 3; y = −x + 3; y = 3x + 1; y = 2x + 3.)

Answer: y = x + 3. The line's slope is 1 (it changes by 1 for each 1 to the right). Parallel lines have equal slopes, so y = x + 3 is parallel.

Slope from a graph (positive, negative, zero, undefined)

Which best describes the slope of the line in the graph? (Choices: Zero; Positive; Negative; Undefined.)

Answer: Positive. The line rises from left to right, so its slope is positive.

Slope from two points

The line through (5, −1) and (10, k) has slope -3. What is the value of k? (Choices: −16; −15; 1; 14.)

Answer: −16. Slope = rise ÷ run, so rise = slope × run = −3 × 5 = −15. Then k = −1 + −15 = −16.

Match a graph to its equation

Which equation matches the line in the graph? (Choices: y = −x + 3; y = 3x + 1; y = x + 3; y = x − 3.)

Answer: y = x + 3. The line crosses the y-axis at 3, so b = 3. Moving 1 to the right, it changes by 1, so m = 1. The equation is y = x + 3.

Rate of change in word problems

A gym charges a one-time sign-up fee plus a fixed amount each month. After 2 months a member has paid $108.00 in total, and after 5 months $195.00. How much is the sign-up fee? (Choices: $79.00; $50.00; $29.00; $21.00.)

Answer: $50.00. Rate of change (slope) = change in cost ÷ change in months = $87.00 ÷ 3 = $29.00 per month. Subtract the monthly charges from the first total to get the starting value: $50.00.

Write the equation of a line

A line has slope -5 and passes through (−4, 1). Which is its equation in slope-intercept form? (Choices: y = 5x − 19; y = −5x + 21; y = −5x + 1; y = −5x − 19.)

Answer: y = −5x − 19. Substitute into y = mx + b: 1 = −5(−4) + b, so b = −19. The equation is y = −5x − 19.

Worked examples

Example 1

Question: The graph shows a line crossing both axes at the marked points. Which equation, in standard form, describes it?

1. 2x − y = −2
2. 2x − y = 2
3. x − 2y = −2
4. 2x + y = 2

How to solve it: The intercepts are (1, 0) and (0, −2). The line x/1 + y/−2 = 1 becomes 2x − y = 2 after clearing fractions.

Answer: 2x − y = 2

Why the other choices don't work:

• A student who picks "2x − y = −2" usually made a sign error on the constant.
• A student who picks "x − 2y = −2" usually put the x-intercept on x and the y-intercept on y (the coefficients are the other way round).
• A student who picks "2x + y = 2" usually made a sign error on the y-term.

Example 2

Question: What is the x-intercept of the line −5x − 3y = 15?

1. (15, 0)
2. (−5, 0)
3. (−3, 0)
4. (3, 0)

How to solve it: For the x-intercept set y = 0: −5x = 15, so x = −3. The point is (−3, 0).

Answer: (−3, 0)

Why the other choices don't work:

• A student who picks "(15, 0)" usually used the constant on the right side of the equation as the intercept.
• A student who picks "(−5, 0)" usually gave the other intercept (mixed up x- and y-intercepts).
• A student who picks "(3, 0)" usually made a sign error.

Common mistakes to watch for

• Question: Which equation is 4x + 4y = 12 written in slope-intercept form? (Choices: y = x + 3; y = −4x + 12; y = −x − 3; y = −x + 3.)

  Answer: y = −x + 3.

  A student who picks "y = x + 3" usually forgot to change the sign of the x-term when moving it across the equals sign.

• Question: Rewrite −4x + 2y = −4 in the form y = mx + b. (Choices: y = −2x − 2; y = 2x + 2; y = 4x − 4; y = 2x − 2.)

  Answer: y = 2x − 2.

  "y = 4x − 4" is a tempting wrong answer — did not divide every term by the coefficient of y.

• Question: Rewrite 15x + 3y = −9 in the form y = mx + b. (Choices: y = −5x − 3; y = 5x − 3; y = −5x + 3; y = −15x − 9.)

  Answer: y = −5x − 3.

  A student who picks "y = −5x + 3" usually made a sign error on the constant term.

• Question: Which equation is a line parallel to the line shown in the graph? (Choices: y = x + 3; y = −x + 3; y = 3x + 1; y = 2x + 3.)

  Answer: y = x + 3.

  A student who picks "y = 3x + 1" usually matched the y-intercept instead of the slope.

• Question: Which best describes the slope of the line in the graph? (Choices: Zero; Positive; Negative; Undefined.)

  Answer: Positive.

  A student who picks "Zero" usually confused a vertical line (undefined slope) with a horizontal line (zero slope).

• Question: The line through (5, −1) and (10, k) has slope -3. What is the value of k? (Choices: −16; −15; 1; 14.)

  Answer: −16.

  A student who picks "1" usually added the slope and the run instead of multiplying them.

Try these practice questions

1. Which equation is 4x + 4y = 12 written in slope-intercept form?

   1. y = x + 3
   2. y = −4x + 12
   3. y = −x − 3
   4. y = −x + 3

2. Rewrite −4x + 2y = −4 in the form y = mx + b.

   1. y = −2x − 2
   2. y = 2x + 2
   3. y = 4x − 4
   4. y = 2x − 2

3. Rewrite 15x + 3y = −9 in the form y = mx + b.

   1. y = −5x − 3
   2. y = 5x − 3
   3. y = −5x + 3
   4. y = −15x − 9

4. What is the x-intercept of the line 4x + 5y = 60?

   1. (15, 0)
   2. (−15, 0)
   3. (12, 0)
   4. (60, 0)

5. Which equation is 20x + 4y = −24 written in slope-intercept form?

   1. y = −5x − 6
   2. y = −20x − 24
   3. y = 5x − 6
   4. y = −5x + 6

6. Which equation is −18x + 3y = 12 written in slope-intercept form?

   1. y = −6x + 4
   2. y = 6x − 4
   3. y = 18x + 12
   4. y = 6x + 4

Answer key

1. y = −x + 3 — Move the x-term: 4y = −4x + 12. Divide every term by 4: y = −x + 3.
2. y = 2x − 2 — Move the x-term: 2y = 4x − 4. Divide every term by 2: y = 2x − 2.
3. y = −5x − 3 — Move the x-term: 3y = −15x − 9. Divide every term by 3: y = −5x − 3.
4. (15, 0) — For the x-intercept set y = 0: 4x = 60, so x = 15. The point is (15, 0).
5. y = −5x − 6 — Move the x-term: 4y = −20x − 24. Divide every term by 4: y = −5x − 6.
6. y = 6x + 4 — Move the x-term: 3y = 18x + 12. Divide every term by 3: y = 6x + 4.

Keep practicing

The fastest way to build confidence is a few questions at a time, with feedback on each answer. Start with Slopes & Linear Equations practice for grade 8, where every question comes with a step-by-step explanation.

More from BAMS Academy:

• All 8th grade math topics
• Algebra 1 practice
• Geometry practice
• BAMS Academy math practice by grade
• Every 8th grade subject